Internal problem ID [2736]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 4.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)+8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right )+c_{3} {\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 41
DSolve[y'''[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-2 x}+e^x \left (c_3 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right )\right ) \\ \end{align*}